<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We consider the simplest parabolic-elliptic model of chemotaxis in the whole space and in several space dimensions. Criteria either for the existence of radial global-in-time solutions or their blowup in terms of suitable Morrey spaces norms are discussed. This is an extended version of the lecture presented at the University of Silesia on January 12, 2018, commemorating Professor Andrzej Lasota-great scholar, master of fine mathematics and applications to real world.</p></abstract>

We consider the simplest parabolic-elliptic model of chemotaxis in the whole space and in several space dimensions. Criteria either for the existence of radial global-in-time solutions or their blowup in terms of suitable Morrey spaces norms are discussed. This is an extended version of the lecture presented at the University of Silesia on January 12, 2018, commemorating Professor Andrzej Lasota-great scholar, master of fine mathematics and applications to real world.

Mathematical Challenges in the Theory of Chemotaxis

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Mathematical Challenges in the Theory of Chemotaxis"}

We consider the simplest parabolic-elliptic model of chemotaxis in the whole space and in several space dimensions. Criteria either for the existence of radial...

Mathematical Challenges in the Theory of Chemotaxis

Published Online: Aug 24, 2018

Page range: 43 - 63

Received: Feb 22, 2018

Accepted: Mar 21, 2018

DOI: https://doi.org/10.2478/amsil-2018-0004

Keywords
chemotaxis, blowup of solutions, global existence of solutions

© 2018 Piotr Biler, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mathematical Challenges in the Theory of Chemotaxis

Published Online: Aug 24, 2018

Page range: 43 - 63

Received: Feb 22, 2018

Accepted: Mar 21, 2018

DOI: https://doi.org/10.2478/amsil-2018-0004

Keywordschemotaxis, blowup of solutions, global existence of solutions

© 2018 Piotr Biler, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
chemotaxis, blowup of solutions, global existence of solutions